I was reading about the ISS earlier, and this question came into my mind, and I can't seem to decided how this actually works. Here's the set-up: Say I have two masses stuck together (m1 and m2) to form a mass M in orbit around some planet (like the ISS, and some large space capsule that is docked with it), and m2 takes off due to an external force (like the capsule flying away without pushing up against the ISS) what happens to the orbit of the mass that didn't take off? I think that if the two masses were pushed apart from each other due to some internal force (like if some giant spring pushed them apart from one another) then they would both move away from each other, and, I think, the center of mass of the new system would continue on in the same orbit as M would have followed (conservation of momentum). But that's not the situation here, since there is an external force applied to one of the masses, but not the other, the momentum of the system is changed. M is tracing an orbit that I think follows a path right through its center of mass. When M breaks apart, m1 would now have a center of mass that doesn't line up with the orbit it is following, which doesn't seem right. On the other hand, there was no force applied to m1 , so I can't see how it would move to line up it's center of mass with it's direction of travel, or change orbits to line its direction of travel up with its center of mass. Orbital mechanics are fun to think about, but boy do they make my head hurt. Can anyone help me out with this?